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Question

It takes $$12$$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for $$9$$ hours, only half the pool is filled. How long would it take for each pipe to fill the pool separately?


Solution

Let the larger pipe fills $$x $$ part of tank in $$1$$ hour
      the smaller pipe fills $$y$$ part of tank in $$1$$ hour
      Volume of tank be $$V$$
From the conditions 
$$12{x}+12{y}=V$$
$$4{x}+9{y}=\dfrac{V}{2}$$

$$\implies x=\dfrac{V}{20},y=\dfrac{V}{30}$$
Time taken by larger pipe to fill the tank is $$\dfrac{V}{x}=\dfrac{V}{\dfrac{V}{20}}=20\ hrs$$

Time taken by smaller pipe to fill the tank is $$\dfrac{V}{y}=\dfrac{V}{\dfrac{V}{30}}=30\ hrs$$

Mathematics

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